Find the domain of $LaTeX: \displaystyle f(x) = \sqrt{8 x - 5} - 19$ . Write the solution in interval notation.

The domain of a radical function is the solution to the inequality radicand $LaTeX: \displaystyle \geq 0$ . The inequality is $LaTeX: \displaystyle 8 x - 5 \geq 0$ . Isolating $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle 8 x \geq 5$ Dividing to finish isolating $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x \geq \frac{5}{8}$ . The domain is $LaTeX: \displaystyle \left[\frac{5}{8}, \infty\right)$